Morera’s theorem and functional series in the class of $A$-analytic functions

The aim of this paper is to investigate $A$-analytic functions in a special case when the function $A$ is an anti-analytic function in a domain. We prove that a continuous function satisfying the integral condition of the Cauchy theorem is $A$-analytic (an analog of Morera's theorem, Sec. 2). In Sec. 3 we prove an analog of the Weierstrass theorem for functional series of $A$-analytic functions and the expansion of $A$-analytic functions into functional series (Sec. 4).